Methodology for the Evaluation of Natural Ventilation in ... - Cham

gLTAr (5.23)2UWhen the flow is driven purely by buoyancy, the reference velocity in the denominator is thebuoyancy velocity, making the Archimedes number equal to 1.It is impossible to match all of the dimensionless parameters that are the result of making thegoverning equations dimensionless. Reducing the scale by a factor of ten will result in anincreased velocity by a factor of 10 to keep the Reynolds number, and a temperature differencefactor of 1,000 to retain the Archimedes number. However, literature states that this can beresolved if the flow is fully developed turbulent flow (Etheridge and Sandberg, 1996). Then theArchimedes number becomes the most relevant to match between the prototype and scale model.When evaluating the dimensionless parameters, the characteristic length selected will have animpact on the Reynolds and Archimedes numbers and therefore influence how the flow regime isdescribed within the model. Popiolek et al (1998) studied the effect of the Reynolds number onsimilarity for models at small (1:10), medium (1:5) and large (1:1.175) scales for a mechanicallyventilated room. They found a critical threshold Reynolds number of 10,000 to 20,000.Similarity is improved when the Reynolds number exceeds 20,000, but doesn‘t substantiallydegrade until the Reynolds number is approximately 2,000. At that point, any discrepanciesbetween the model and prototype become evident.5.3.3 Thermal SimilarityThe requirement of thermal similarity is met when the temperature differences and patterns arecomparable. Thermal similarity is achieved with similar heat flows and distribution through themodeled space. The model and prototype temperatures are compared using the referencetemperature difference calculated using equation 5.12. Using the non-dimensionalizedtemperature of the model and the appropriate reference temperature for the prototype, thecorresponding prototype temperature difference for a specific location can be determined, andvice versa.TTTT (5.24)TrefTrefMP5.4 Other Issues for SimilarityThe same similarity requirements discussed above also apply to the boundary conditions. Thegeometric boundary conditions are achieved if overall geometric similarity is satisfied. The inletair velocity and flow pattern will be similar if the inlet opening and surface roughness are similarin the model and prototype, achieving kinematic similarity at the boundary. Thermal similarityis the most difficult of the three to achieve at the boundary conditions. At the boundary, the heatflux, distribution of surface temperatures and radiation all must be considered and evaluatedbetween the model and prototype. If the Ar, Re, and Pr numbers are not matched, it isimpossible to match the surface temperature distributions between the prototype and model.88